On the Basic Representation Theorem for Convex Domination of Measures
NOTE: At the time of publication, the author Theodore P. Hill was not yet affiliated with Cal Poly.
A direct, constructive proof is given for the basic representation theorem for convex domination of measures. The proof is given in the finitistic case (purely atomic measures with a finite number of atoms), and a simple argument is then given to extend this result to the general case, including both probability measures and finite Borel measures on infinite-dimensional spaces. The infinite-dimensional case follows quickly from the finite-dimensional case with the use of the approximation property.
J. Elton and Theodore P. Hill. "On the Basic Representation Theorem for Convex Domination of Measures" Journal of Mathematical Analysis and Applications 228.2 (1998): 449-466.
Available at: http://works.bepress.com/tphill/62